This cycle’s Republican presidential primary was notable for its historic volatility and sheer unpredictability—as would be any contest featuring the improbable rise (and inevitable fall) of Michele Bachmann, Herman Cain, Newt Gingrich, and Rick Santorum. Even Donald Trump, the nation’s chief “birther” and No. 1 self-promoter, briefly led a national poll or two.

Still, compared with the chaos that might envelope the party four years hence, Republicans could be left yearning for those simpler times.

The GOP, with the possible exception of vice presidential nominee Paul Ryan, who has said he will return to the House, doesn’t have an heir apparent. That alone is a disorienting prospect for a party that has traditionally anointed a previous primary challenger, the next-in-line candidate, to become its standard-bearer four years later—as was the case for Romney this year.

More broadly, however, that fearsome sense of the unknown is tied to the party’s future course. Will party members come to believe, as some conservatives are already arguing, that the GOP’s past two nominees have been insufficiently conservative? Or will they mandate that their next presidential nominee find a way to broaden the party’s appeal, particularly among minorities, even if that requires a softening of conservative doctrine? The Republican candidates will become vessels of these competing beliefs and others.

One thing that Republicans can feel good about: Even if the next presidential primary looks unpredictable, their bench of hopefuls is much deeper and more talented, and they are likely better able to connect with a wider swath of voters than the last contenders.

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There’s Ryan, who, despite having been a part of a failed ticket, managed to raise his national profile during the last few months; he remains a fresh face and well-regarded within the Republican Party as an intellectual force. Former Florida Gov. Jeb Bush, although still burdened by his family name, has nonetheless earned a reputation as a wise man and a pragmatist within the GOP who early on sounded the alarm over the party’s growing Latino problem.

New Jersey’s straight-talking, budget-slashing Chris Christie has become a national GOP favorite since becoming the Garden State’s governor in 2009. Despite being one of the most oft-deployed and hardest-hitting Romney surrogates, Christie had nothing but warm words for President Obama in the closing days of the race and is governing with a high approval rating in a blue state. Although that might hurt while he’s trying to barrel through a GOP primary, what Republicans might be craving after Romney is a little bit of authenticity.

“We need people who can speak to a modern audience in a forthright, honest way so when our candidates talk, voters think they’ve learned something ... not full of cliché, hokey, tired talking points,” said GOP consultant Ed Rogers. “Romney didn’t speak to a modern audience very well; he just didn’t.”

Then there are the candidates who would help the GOP rebrand itself as not just the party of old white men, a classification that stings more and more with each passing election cycle as minorities, young people, and women compound their importance in the electorate. “Right now, [Republicans] have a national coalition that is limited,” said former Rep. Tom Davis of Virginia, a moderate Republican. “They’re going to have to expand their footprint to some of these minority groups. We have not done a good job of reaching out there.”

Among those who would help in broadening the GOP coalition: Sen. Marco Rubio of Florida, a Cuban-American and lauded orator who electrified the crowd with his speech at the Republican National Convention; New Mexico Gov. Susana Martinez, a Mexican-American from a middle-class background; Louisiana Gov. Bobby Jindal, an Indian-American conservative with a penchant for wonkery; South Carolina Gov. Nikki Haley, who was another active surrogate for the Romney campaign and even incoming Sen. Ted Cruz of Texas, another Cuban-American.

But don’t count social conservatives out. In the eyes of these activists, what the party really needs is a true conservative nominee. Santorum, the second-place primary finisher, is planting the seeds for a future run by remaining actively involved with his political action committee, Patriot Voices, and making frequent visits to Iowa, South Carolina, and other early primary states. Indiana Gov.-elect Mike Pence and Sen. Rand Paul of Kentucky, both popular with the tea party, also populate the wish-lists of many conservatives.

SEEKING A SUCCESSOR

Democrats, meanwhile, will be contemplating the particular challenges of securing the presidency for a third consecutive term—an unusual feat that has been accomplished only once since World War II, by George H.W. Bush, who then failed to make it four in a row.

Pundits have to follow a certain order of operations to determine what a prospective Democratic field would look like. And, undoubtedly, the first step is answering the question that has percolated in Washington for years: What will Hillary Rodham Clinton do?